Site preference of chalcogen atoms in 1T$^\prime$ $MX_{2(1-x)}Y_{2x}$ ($M=$ Mo and W; $X, Y=$ S, Se, and Te)
The insulator-metal transition, accompanying the structural phase transition from 2H to 1T$^\prime$ structure, has been reported in two-dimensional W-S-Te and W-Se-Te systems. It is also reported that Te atoms tend to occupy a specific site of the 1T$^\prime$ structure. Here, we study the site preference of chalcogen atoms in $MX_{2(1-x)}Y_{2x}$ ($M=$ Mo and W; $X, Y=$ S, Se, and Te; $0\le x \le 1$) using first-principles approach. We demonstrate that the site preference of chalcogen atoms explains the universal correlation between the formation energy and the Peierls-like distortion amplitude in the 1T$^\prime$ phase. The impact of the site preference on the linear elastic properties is strong, whereas its impact is weak in the non-linear regime. This establishes the structure-property relationships in $MX_{2(1-x)}Y_{2x}$ systems.